abstract = "Drift towards growing size of genotypes is one
outstanding and constantly disputed invariant in an
overwhelming number of applications of evolutionary
algorithms with variable-size structures. In contrast
to previous work to reveal its fundamentals, we
probabilistically analyse genotype growth by building
on the idea of a 'representation-less' model by Banzhaf
and Langdon. Our model, called the fitness-size model,
corresponds to a simple evolutionary algorithm using
overproduction selection and mutation working on
abstract objects retaining only fitness and size
information.

The probalistic analysis offer some surprises counter
to present credence. The analysis predicts that average
effective and noneffective lengths (and thus overall
size) tend to be invariant over time. The same is true
for the variance of the effective length. In contrast,
the variance of the noneffective size features
increases linearly in time, and its variation shows the
trademark of a diffusion process.Drift to increasing
size manifest s if search biases favour boundary
conditions. We present experimental results with both
the implementation of the theoretical model and a
standard genetic programming algorithm. Statistical
results with the two implementations are similar and
fit the theoretical predictions.",